# -*- coding: utf-8 -*-
# ------------------------------------------------------------------------------
# Name:         serial.py
# Purpose:      music21 classes for serial transformations
#
# Authors:      Michael Scott Cuthbert
#               Christopher Ariza
#
# Copyright:    Copyright © 2009-2012 Michael Scott Cuthbert and the music21 Project
# License:      BSD, see license.txt
# ------------------------------------------------------------------------------
'''
This module defines objects for defining and manipulating structures
common to serial and/or twelve-tone music,
including :class:`~music21.serial.ToneRow` subclasses.

Serial searching methods that were previously here have been moved to `alpha.search.serial`
'''

import unittest
import copy
from typing import Union, List, Any

from music21 import exceptions21

from music21 import note
from music21 import chord
from music21 import stream
from music21 import pitch

from music21 import environment

_MOD = 'serial'
environLocal = environment.Environment(_MOD)


# ------------------------------------------------------------------------------
class SerialException(exceptions21.Music21Exception):
    pass


# ------------------------------------------------------------------------------
class TwelveToneMatrix(stream.Stream):
    '''
    An object representation of a 2-dimensional array of 12 pitches.
    Internal representation is as a :class:`~music21.stream.Stream`,
    which stores 12 Streams, each Stream a horizontal row of pitches
    in the matrix.

    This object is commonly used by calling the
    :meth:`~music21.stream.TwelveToneRow.matrix` method of
    :meth:`~music21.stream.TwelveToneRow` (or a subclass).

    >>> ttr = serial.TwelveToneRow([0, 2, 11, 7, 8, 3, 9, 1, 4, 10, 6, 5])
    >>> aMatrix = ttr.matrix()
    >>> print(aMatrix)
      0  2  B  7  8  3  9  1  4  A  6  5
      A  0  9  5  6  1  7  B  2  8  4  3
      1  3  0  8  9  4  A  2  5  B  7  6
      5  7  4  0  1  8  2  6  9  3  B  A
      4  6  3  B  0  7  1  5  8  2  A  9
      9  B  8  4  5  0  6  A  1  7  3  2
      3  5  2  A  B  6  0  4  7  1  9  8
      B  1  A  6  7  2  8  0  3  9  5  4
      8  A  7  3  4  B  5  9  0  6  2  1
      2  4  1  9  A  5  B  3  6  0  8  7
      6  8  5  1  2  9  3  7  A  4  0  B
      7  9  6  2  3  A  4  8  B  5  1  0

    >>> repr(aMatrix)
    '<music21.serial.TwelveToneMatrix for [<music21.serial.TwelveToneRow row-1>]>'

    >>> fourthQuartetMatrix = serial.getHistoricalRowByName('SchoenbergOp37').matrix()
    >>> repr(fourthQuartetMatrix)
    '<music21.serial.TwelveToneMatrix for
         [<music21.serial.HistoricalTwelveToneRow Schoenberg Op. 37 Fourth String Quartet>]>'
    '''

    def __str__(self):
        '''
        Return a string representation of the matrix.
        '''
        ret = []
        for rowForm in self:
            msg = []
            for n in rowForm:
                msg.append(str(n.pitch.pitchClassString).rjust(3))
            ret.append(''.join(msg))
        return '\n'.join(ret)

    def _reprInternal(self):
        if self:
            if isinstance(self[0], ToneRow):
                return f'for [{self[0]}]'
            else:
                return super()._reprInternal()
        else:
            return super()._reprInternal()
# ------------------------------------------------------------------------------


# noinspection SpellCheckingInspection
historicalDict = {
    'WebernOp29': ('Webern', 'Op. 29', 'Cantata I',
                        [3, 11, 2, 1, 5, 4, 7, 6, 10, 9, 0, 8]),
    'WebernOp28': ('Webern', 'Op. 28', 'String Quartet',
                        [1, 0, 3, 2, 6, 7, 4, 5, 9, 8, 11, 10]),
    'SchoenbergOp24Mvmt5': ('Schoenberg', 'Op. 24', 'Serenade, Mvt. 5, "Tanzscene"',
                                 [9, 10, 0, 3, 4, 6, 5, 7, 8, 11, 1, 2]),
    'SchoenbergOp24Mvmt4': ('Schoenberg', 'Op. 24', 'Serenade, Mvt. 4, "Sonett"',
                                 [4, 2, 3, 11, 0, 1, 8, 6, 9, 5, 7, 10]),
    'SchoenbergJakobsleiter': ('Schoenberg', None, 'Die Jakobsleiter',
                                    [1, 2, 5, 4, 8, 7, 0, 3, 11, 10, 6, 9]),
    'SchoenbergOp27No4': ('Schoenberg', 'Op. 27 No. 4', 'Four Pieces for Mixed Chorus, No. 4',
                               [1, 3, 10, 6, 8, 4, 11, 0, 2, 9, 5, 7]),
    'WebernOp23': ('Webern', 'Op. 23', 'Three Songs',
                        [8, 3, 7, 4, 10, 6, 2, 5, 1, 0, 9, 11]),
    'BergLuluActIIScene1': ('Berg', 'Lulu, Act II, Scene 1',
                                 'Perm. (Every 5th Note Of Transposed Primary Row)',
                                 [10, 7, 1, 0, 9, 2, 4, 11, 5, 8, 3, 6]),
    'SchoenbergOp27No1': ('Schoenberg', 'Op. 27 No. 1', 'Four Pieces for Mixed Chorus, No. 1',
                               [6, 5, 2, 8, 7, 1, 3, 4, 10, 9, 11, 0]),
    'BergLuluActIScene20': ('Berg', 'Lulu, Act I , Scene XX',
                                 'Perm. (Every 7th Note Of Transposed Primary Row)',
                                 [10, 6, 3, 8, 5, 11, 4, 2, 9, 0, 1, 7]),
    'SchoenbergOp27No3': ('Schoenberg', 'Op. 27 No. 3', 'Four Pieces for Mixed Chorus, No. 3',
                               [7, 6, 2, 4, 5, 3, 11, 0, 8, 10, 9, 1]),
    'SchoenbergOp27No2': ('Schoenberg', 'Op. 27 No. 2', 'Four Pieces for Mixed Chorus, No. 2',
                               [0, 11, 4, 10, 2, 8, 3, 7, 6, 5, 9, 1]),
    'SchoenbergFragPiano': ('Schoenberg', None, 'Fragment For Piano',
                                 [6, 9, 0, 7, 1, 2, 8, 11, 5, 10, 4, 3]),
    'SchoenbergOp50B': ('Schoenberg', 'Op. 50B', 'De Profundis',
                             [3, 9, 8, 4, 2, 10, 7, 11, 0, 6, 5, 1]),
    'SchoenbergOp50C': ('Schoenberg', 'Op. 50C', 'Modern Psalms, The First Psalm',
                             [4, 3, 0, 8, 11, 7, 5, 9, 6, 10, 1, 2]),
    'SchoenbergOp50A': ('Schoenberg', 'Op. 50A', 'Three Times A Thousand Years',
                             [7, 9, 6, 4, 5, 11, 10, 2, 0, 1, 3, 8]),
    'SchoenbergMosesAron': ('Schoenberg', None, 'Moses And Aron',
                                 [9, 10, 4, 2, 3, 1, 7, 5, 6, 8, 11, 0]),
    'WebernOp25': ('Webern', 'Op. 25', 'Three Songs',
                        [7, 4, 3, 6, 1, 5, 2, 11, 10, 0, 9, 8]),
    'SchoenbergOp23No5': ('Schoenberg', 'Op. 23, No. 5', 'Five Piano Pieces',
                               [1, 9, 11, 7, 8, 6, 10, 2, 4, 3, 0, 5]),
    'SchoenbergOp28No1': ('Schoenberg', 'Op. 28 No. 1',
                               'Three Satires for Mixed Chorus, No. 1',
                               [0, 4, 7, 1, 9, 11, 5, 3, 2, 6, 8, 10]),
    'SchoenbergOp28No3': ('Schoenberg', 'Op. 28 No. 3',
                               'Three Satires for Mixed Chorus, No. 3',
                               [5, 6, 4, 8, 2, 10, 7, 9, 3, 11, 1, 0]),
    'WebernOp21': ('Webern', 'Op. 21', 'Chamber Symphony',
                        [5, 8, 7, 6, 10, 9, 3, 4, 0, 1, 2, 11]),
    'SchoenbergIsraelExists': ('Schoenberg', None, 'Israel Exists Again',
                                    [0, 3, 4, 9, 11, 5, 2, 1, 10, 8, 6, 7]),
    'SchoenbergOp35No2': ('Schoenberg', 'Op. 35', 'Six Pieces for Male Chorus, No. 2',
                               [6, 9, 7, 1, 0, 2, 5, 11, 10, 3, 4, 8]),
    'SchoenbergOp35No3': ('Schoenberg', 'Op. 35', 'Six Pieces for Male Chorus, No. 3',
                               [3, 6, 7, 8, 5, 0, 9, 10, 4, 11, 2, 1]),
    'SchoenbergOp35No1': ('Schoenberg', 'Op. 35', 'Six Pieces for Male Chorus, No. 1',
                               [2, 11, 3, 5, 4, 1, 8, 10, 9, 6, 0, 7]),
    'SchoenbergOp48No1': ('Schoenberg', 'Op. 48', 'Three Songs, No. 1, "Sommermud"',
                               [1, 2, 0, 6, 3, 5, 4, 10, 11, 7, 9, 8]),
    'SchoenbergOp35No5': ('Schoenberg', 'Op. 35', 'Six Pieces for Male Chorus, No. 5',
                               [1, 7, 10, 2, 3, 11, 8, 4, 0, 6, 5, 9]),
    'SchoenbergOp29': ('Schoenberg', 'Op. 29', 'Suite',
                            [3, 7, 6, 10, 2, 11, 0, 9, 8, 4, 5, 1]),
    'BergLyricSuitePerm': ('Berg', None, 'Lyric Suite, Last Mvt. Permutation',
                                [5, 6, 10, 4, 1, 9, 2, 8, 7, 3, 0, 11]),
    'WebernOp20': ('Webern', 'Op. 20', 'String Trio',
                        [8, 7, 2, 1, 6, 5, 9, 10, 3, 4, 0, 11]),
    'SchoenbergOp46': ('Schoenberg', 'Op. 46', 'A Survivor From Warsaw',
                            [6, 7, 0, 8, 4, 3, 11, 10, 5, 9, 1, 2]),
    'SchoenbergFragOrganSonata': ('Schoenberg', None, 'Fragment of Sonata For Organ',
                                       [1, 7, 11, 3, 9, 2, 8, 6, 10, 5, 0, 4]),
    'SchoenbergOp44': ('Schoenberg', 'Op. 44', 'Prelude To A Suite From "Genesis"',
                            [10, 6, 2, 5, 4, 0, 11, 8, 1, 3, 9, 7]),
    'SchoenbergOp45': ('Schoenberg', 'Op. 45', 'String Trio',
                            [2, 10, 3, 9, 4, 1, 11, 8, 6, 7, 5, 0]),
    'SchoenbergOp33A': ('Schoenberg', 'Op. 33A', 'Two Piano Pieces, No. 1',
                             [10, 5, 0, 11, 9, 6, 1, 3, 7, 8, 2, 4]),
    'SchoenbergOp25': ('Schoenberg', 'Op.25', 'Suite for Piano',
                            [4, 5, 7, 1, 6, 3, 8, 2, 11, 0, 9, 10]),
    'SchoenbergOp26': ('Schoenberg', 'Op. 26', 'Wind Quintet',
                            [3, 7, 9, 11, 1, 0, 10, 2, 4, 6, 8, 5]),
    'SchoenbergOp33B': ('Schoenberg', 'Op. 33B', 'Two Piano Pieces, No. 2',
                             [11, 1, 5, 3, 9, 8, 6, 10, 7, 4, 0, 2]),
    'BergViolinConcerto': ('Berg', None, 'Concerto For Violin And Orchestra',
                                [7, 10, 2, 6, 9, 0, 4, 8, 11, 1, 3, 5]),
    'WebernOp22': ('Webern', 'Op. 22', 'Quartet For Violin, Clarinet, Tenor Sax, And Piano',
                        [6, 3, 2, 5, 4, 8, 9, 10, 11, 1, 7, 0]),
    'BergLulu': ('Berg', None, 'Lulu: Primary Row',
                        [0, 4, 5, 2, 7, 9, 6, 8, 11, 10, 3, 1]),
    'WebernOp30': ('Webern', 'Op. 30', 'Variations For Orchestra',
                        [9, 10, 1, 0, 11, 2, 3, 6, 5, 4, 7, 8]),
    'WebernOp31': ('Webern', 'Op. 31', 'Cantata II',
                        [6, 9, 5, 4, 8, 3, 7, 11, 10, 2, 1, 0]),
    'WebernOpNo17No1': ('Webern', 'Op. 17, No. 1', '"Armer Sunder, Du"',
                             [11, 10, 5, 6, 3, 4, 7, 8, 9, 0, 1, 2]),
    'WebernOp24': ('Webern', 'Op. 24', 'Concerto For Nine Instruments',
                        [11, 10, 2, 3, 7, 6, 8, 4, 5, 0, 1, 9]),
    'SchoenbergOp48No2': ('Schoenberg', 'Op. 48', 'Three Songs, No. 2, "Tot"',
                               [2, 3, 9, 1, 10, 4, 8, 7, 0, 11, 5, 6]),
    'WebernOp27': ('Webern', 'Op. 27', 'Variations For Piano',
                        [3, 11, 10, 2, 1, 0, 6, 4, 7, 5, 9, 8]),
    'SchoenbergOp47': ('Schoenberg', 'Op. 47', 'Fantasy For Violin And Piano',
                            [10, 9, 1, 11, 5, 7, 3, 4, 0, 2, 8, 6]),
    'WebernOp19No2': ('Webern', 'Op. 19, No. 2', '"Ziehn Die Schafe"',
                           [8, 4, 9, 6, 7, 0, 11, 5, 3, 2, 10, 1]),
    'WebernOp19No1': ('Webern', 'Op. 19, No. 1', '"Weiss Wie Lilien"',
                           [7, 10, 6, 5, 3, 9, 8, 1, 2, 11, 4, 0]),
    'WebernOp26': ('Webern', 'Op. 26', 'Das Augenlicht',
                        [8, 10, 9, 0, 11, 3, 4, 1, 5, 2, 6, 7]),
    'SchoenbergFragPianoPhantasia': ('Schoenberg', None, 'Fragment of Phantasia For Piano',
                                          [1, 5, 3, 6, 4, 8, 0, 11, 2, 9, 10, 7]),
    'BergDerWein': ('Berg', None, 'Der Wein',
                         [2, 4, 5, 7, 9, 10, 1, 6, 8, 0, 11, 3]),
    'BergWozzeckPassacaglia': ('Berg', None, 'Wozzeck, Act I, Scene 4 "Passacaglia"',
                                    [3, 11, 7, 1, 0, 6, 4, 10, 9, 5, 8, 2]),
    'WebernOp18No1': ('Webern', 'Op. 18, No. 1', '"Schatzerl Klein"',
                           [0, 11, 5, 8, 10, 9, 3, 4, 1, 7, 2, 6]),
    'WebernOp18No2': ('Webern', 'Op. 18, No. 2', '"Erlosung"',
                           [6, 9, 5, 8, 4, 7, 3, 11, 2, 10, 1, 0]),
    'WebernOp18No3': ('Webern', 'Op. 18, No. 3', '"Ave, Regina Coelorum"',
                           [4, 3, 7, 6, 5, 11, 10, 2, 1, 0, 9, 8]),
    'SchoenbergOp42': ('Schoenberg', 'Op. 42', 'Concerto For Piano And Orchestra',
                            [3, 10, 2, 5, 4, 0, 6, 8, 1, 9, 11, 7]),
    'SchoenbergOp48No3': ('Schoenberg', 'Op. 48', 'Three Songs, No, 3, "Madchenlied"',
                               [1, 7, 9, 11, 3, 5, 10, 6, 4, 0, 8, 2]),
    'SchoenbergOp37': ('Schoenberg', 'Op. 37', 'Fourth String Quartet',
                            [2, 1, 9, 10, 5, 3, 4, 0, 8, 7, 6, 11]),
    'SchoenbergOp36': ('Schoenberg', 'Op. 36', 'Concerto for Violin and Orchestra',
                            [9, 10, 3, 11, 4, 6, 0, 1, 7, 8, 2, 5]),
    'SchoenbergOp34': ('Schoenberg', 'Op. 34', 'Accompaniment to a Film Scene',
                            [3, 6, 2, 4, 1, 0, 9, 11, 10, 8, 5, 7]),
    'BergChamberConcerto': ('Berg', None, 'Chamber Concerto',
                                 [11, 7, 5, 9, 2, 3, 6, 8, 0, 1, 4, 10]),
    'SchoenbergOp32': ('Schoenberg', 'Op. 32', 'Von Heute Auf Morgen',
                            [2, 3, 9, 1, 11, 5, 8, 7, 4, 0, 10, 6]),
    'SchoenbergOp31': ('Schoenberg', 'Op. 31', 'Variations for Orchestra',
                            [10, 4, 6, 3, 5, 9, 2, 1, 7, 8, 11, 0]),
    'SchoenbergOp30': ('Schoenberg', 'Op. 30', 'Third String Quartet',
                            [7, 4, 3, 9, 0, 5, 6, 11, 10, 1, 8, 2]),
    'BergLyricSuite': ('Berg', None, 'Lyric Suite Primary Row',
                            [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11]),
    'SchoenbergOp41': ('Schoenberg', 'Op. 41', 'Ode To Napoleon',
                            [1, 0, 4, 5, 9, 8, 3, 2, 6, 7, 11, 10]),
    'WebernOp17No3': ('Webern', 'Op. 17, No. 3', '"Heiland, Unsere Missetaten..."',
                           [8, 5, 4, 3, 7, 6, 0, 1, 2, 11, 10, 9]),
    'WebernOp17No2': ('Webern', 'Op. 17, No. 2', '"Liebste Jungfrau"',
                           [1, 0, 11, 7, 8, 2, 3, 6, 5, 4, 9, 10])
}

# ------------------------------------------------------------------------------


class ToneRow(stream.Stream):
    '''
    A Stream representation of a tone row, or an ordered sequence of pitches;
    can most importantly be used to deal with
    serial transformations.

    Unlike a normal Stream, the first argument is assumed to be a ToneRow:

    >>> t = serial.ToneRow([10, 9, 4, 5, 6, 3, 2, 8, 7, 11, 0, 1])

    The representation of a ToneRow will be the contents:

    >>> t
    <music21.serial.ToneRow A94563287B01>

    Unless (like a Stream), the id is set:

    >>> t.id = 'retrograde_jungfrau'
    >>> t
    <music21.serial.ToneRow retrograde_jungfrau>

    A ToneRow does not need to have twelve pitches, like this ten-tone row
    from Ruth Crawford Seeger's String Quartet 1931

    >>> rcsRow = serial.ToneRow([2, 4, 5, 3, 6, 9, 8, 7, 1, 0])
    >>> rcsRow
    <music21.serial.ToneRow 2453698710>
    >>> len(rcsRow)
    10
    '''
    _DOC_ATTR = {
        'row': 'A list representing the pitch class values of the row.',
    }

    _DOC_ORDER = ['pitchClasses', 'noteNames', 'isTwelveToneRow', 'isSameRow',
                  'getIntervalsAsString',
                  'zeroCenteredTransformation', 'originalCenteredTransformation',
                  'findZeroCenteredTransformations', 'findOriginalCenteredTransformations']

    def __init__(self, row=None, *arguments, **keywords):
        super().__init__(*arguments, **keywords)
        if row is not None:
            self.row = row
        else:
            self.row = []

        for pc in self.row:
            if not isinstance(pc, (pitch.Pitch, note.Note)):
                pc = pitch.Pitch(pc)

            if not isinstance(pc, note.Note):
                n = note.Note(pitch=pc)
            else:
                n = pc

            n.pitch.octave = None
            self.append(n)

    def _reprInternal(self):
        superInternal = super()._reprInternal()
        if not superInternal.startswith('0x'):
            return superInternal

        return ''.join(n.pitch.pitchClassString for n in self)

    def pitchClasses(self):
        '''
        Convenience function showing the pitch classes of a
        :class:`~music21.serial.ToneRow` as a list.

        >>> fiveFold = [5 * i for i in range(12)]
        >>> fiveFold
        [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55]

        >>> quintupleRow = serial.pcToToneRow(fiveFold)
        >>> quintupleRow
        <music21.serial.TwelveToneRow 05A3816B4927>
        >>> quintupleRow.pitchClasses()
        [0, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7]

        >>> halfStep = serial.pcToToneRow([0, 1])
        >>> halfStep.pitchClasses()
        [0, 1]
        '''
        pitchList = [n.pitch.pitchClass for n in self]
        return pitchList

    def noteNames(self):
        '''
        Convenience function showing the note names of a
        :class:`~music21.serial.ToneRow` as a list.

        >>> chromatic = serial.TwelveToneRow(range(12))
        >>> chromatic.noteNames()
        ['C', 'C#', 'D', 'E-', 'E', 'F', 'F#', 'G', 'G#', 'A', 'B-', 'B']

        >>> halfStep = serial.ToneRow([0, 1])
        >>> halfStep.noteNames()
        ['C', 'C#']
        '''
        noteList = [p.name for p in self]
        return noteList

    def isTwelveToneRow(self):
        '''
        Describes whether or not a :class:`~music21.serial.ToneRow` constitutes
        a twelve-tone row. Note that a
        :class:`~music21.serial.TwelveToneRow` object might not be a twelve-tone row.

        >>> serial.ToneRow([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]).isTwelveToneRow()
        True
        >>> serial.ToneRow([0, 4, 8]).isTwelveToneRow()
        False
        >>> serial.ToneRow([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]).isTwelveToneRow()
        False
        '''
        pitchList = self.pitchClasses()
        if len(pitchList) != 12:
            return False
        else:
            temp = True
            for i in range(12):
                if i not in pitchList:
                    temp = False
            return temp

    def makeTwelveToneRow(self):
        '''
        Convenience function returning a :class:`~music21.serial.TwelveToneRow` with the
        same pitches.
        Note that a :class:`~music21.serial.ToneRow` may be created without being a
        true twelve tone row.

        >>> r1 = serial.pcToToneRow(range(11))
        >>> type(r1)
        <class 'music21.serial.ToneRow'>
        >>> n = note.Note()
        >>> n.pitch.pitchClass = 11
        >>> r1.append(n)
        >>> r2 = r1.makeTwelveToneRow()
        >>> type(r2)
        <class 'music21.serial.TwelveToneRow'>
        '''
        pcSet = self.pitchClasses()
        a = TwelveToneRow()
        for thisPc in pcSet:
            n = note.Note()
            n.duration.quarterLength = 0.0
            n.pitch.pitchClass = thisPc
            n.pitch.octave = None
            a.append(n)
        return a

    def isSameRow(self, row):
        '''
        Convenience function describing if two rows are the same.

        >>> row1 = serial.pcToToneRow([6, 7, 8])
        >>> row2 = serial.pcToToneRow([-6, 19, 128])
        >>> row3 = serial.pcToToneRow([6, 7, -8])
        >>> row1.isSameRow(row2)
        True
        >>> row2.isSameRow(row1)
        True
        >>> row1.isSameRow(row3)
        False
        '''
        if len(row) != len(self):
            return False
        else:
            tempSame = True
            for i in range(len(row)):
                if tempSame is True:
                    if self[i].pitch.pitchClass != row[i].pitch.pitchClass:
                        tempSame = False

        return tempSame

    def getIntervalsAsString(self):
        '''

        Returns the string of intervals between consecutive pitch classes of
        a :class:`~music21.serial.ToneRow`.
        'T' = 10, 'E' = 11.

        >>> cRow = serial.pcToToneRow([0])
        >>> cRow.getIntervalsAsString()
        ''
        >>> reverseChromatic = serial.pcToToneRow([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
        >>> reverseChromatic.getIntervalsAsString()
        'EEEEEEEEEEE'
        '''
        numPitches = len(self)
        pitchList = self.pitchClasses()
        intervalString = ''
        for i in range(numPitches - 1):
            interval = (pitchList[i + 1] - pitchList[i]) % 12
            if interval in range(10):
                intervalString = intervalString + str(interval)
            if interval == 10:
                intervalString = intervalString + 'T'
            if interval == 11:
                intervalString = intervalString + 'E'
        return intervalString

    def zeroCenteredTransformation(self, transformationType, index):
        '''
        Returns a :class:`~music21.serial.ToneRow` giving a transformation of a tone row.
        Admissible transformationTypes are 'P' (prime), 'I' (inversion),
        'R' (retrograde), and 'RI' (retrograde inversion).

        In the "zero-centered" convention,
        the transformations Pn and In start on the pitch class n, and the transformations
        Rn and RIn end on the pitch class n.

        >>> chromatic = serial.pcToToneRow(range(12))
        >>> chromatic.pitchClasses()
        [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
        >>> chromaticP3 = chromatic.zeroCenteredTransformation('P',3)
        >>> chromaticP3.pitchClasses()
        [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2]
        >>> chromaticI6 = chromatic.zeroCenteredTransformation('I',6)
        >>> chromaticI6.pitchClasses()
        [6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7]
        >>> schoenberg = serial.getHistoricalRowByName('SchoenbergOp26')
        >>> schoenberg.pitchClasses()
        [3, 7, 9, 11, 1, 0, 10, 2, 4, 6, 8, 5]
        >>> schoenbergR8 = schoenberg.zeroCenteredTransformation('R',8)
        >>> schoenbergR8.pitchClasses()
        [10, 1, 11, 9, 7, 3, 5, 6, 4, 2, 0, 8]
        >>> schoenbergRI9 = schoenberg.zeroCenteredTransformation('RI',9)
        >>> schoenbergRI9.noteNames()
        ['G', 'E', 'F#', 'G#', 'B-', 'D', 'C', 'B', 'C#', 'E-', 'F', 'A']
        '''
        numPitches = len(self)
        pitchList = self.pitchClasses()
        if int(index) != index:
            raise SerialException('Transformation must be by an integer.')

        firstPitch = pitchList[0]
        transformedPitchList = []
        if transformationType in ('P', 'T'):
            for i in range(numPitches):
                newPitch = (pitchList[i] - firstPitch + index) % 12
                transformedPitchList.append(newPitch)
        elif transformationType == 'I':
            for i in range(numPitches):
                newPitch = (index + firstPitch - pitchList[i]) % 12
                transformedPitchList.append(newPitch)
        elif transformationType == 'R':
            for i in range(numPitches):
                newPitch = (index + pitchList[numPitches - 1 - i] - firstPitch) % 12
                transformedPitchList.append(newPitch)
        elif transformationType == 'RI':
            for i in range(numPitches):
                newPitch = (index - pitchList[numPitches - 1 - i] + firstPitch) % 12
                transformedPitchList.append(newPitch)
        else:
            raise SerialException(f'Invalid transformation type: {transformationType}')

        return pcToToneRow(transformedPitchList)

    def originalCenteredTransformation(self, transformationType: str, index: int):
        '''
        Returns a :class:`~music21.serial.ToneRow` giving a transformation of a tone row.
        Admissible transformations are 'T' (transposition), 'I' (inversion),
        'R' (retrograde), and 'RI' (retrograde inversion).

        In the "original-centered" convention,
        which is less common than the "zero-centered" convention, the original row is not initially
        transposed to start on the pitch class 0. Thus, the transformation Tn transposes
        the original row up by n semitones, and the transformations In, Rn, and RIn first
        transform the row appropriately (without transposition), then transpose the resulting
        row by n semitones.


        >>> chromatic = serial.pcToToneRow(range(12))
        >>> chromatic.pitchClasses()
        [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
        >>> chromaticP3 = chromatic.originalCenteredTransformation('T',3)
        >>> chromaticP3.pitchClasses()
        [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2]
        >>> chromaticI6 = chromatic.originalCenteredTransformation('I',6)
        >>> chromaticI6.pitchClasses()
        [6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7]
        >>> schoenberg = serial.getHistoricalRowByName('SchoenbergOp26')
        >>> schoenberg.pitchClasses()
        [3, 7, 9, 11, 1, 0, 10, 2, 4, 6, 8, 5]
        >>> schoenbergR8 = schoenberg.originalCenteredTransformation('R',8)
        >>> schoenbergR8.pitchClasses()
        [1, 4, 2, 0, 10, 6, 8, 9, 7, 5, 3, 11]
        >>> schoenbergRI9 = schoenberg.originalCenteredTransformation('RI',9)
        >>> schoenbergRI9.noteNames()
        ['B-', 'G', 'A', 'B', 'C#', 'F', 'E-', 'D', 'E', 'F#', 'G#', 'C']
        '''
        pitchList = self.pitchClasses()
        firstPitch = pitchList[0]
        newIndex = (firstPitch + index) % 12
        if transformationType in ('P', 'T'):
            return self.zeroCenteredTransformation('P', newIndex)

        return self.zeroCenteredTransformation(transformationType, newIndex)

    def findZeroCenteredTransformations(self, otherRow) -> Union[bool, List[Any]]:
        '''
        Gives the list of zero-centered serial transformations
        taking one :class:`~music21.serial.ToneRow`
        to another, the second specified in the argument. Each transformation is given as a
        tuple of the transformation type and index.

        See :meth:`~music21.serial.zeroCenteredTransformation` for
        an explanation of this convention.


        >>> chromatic = serial.pcToToneRow([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1])
        >>> reverseChromatic = serial.pcToToneRow([8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9])
        >>> chromatic.findZeroCenteredTransformations(reverseChromatic)
        [('I', 8), ('R', 9)]
        >>> schoenberg25 = serial.getHistoricalRowByName('SchoenbergOp25')
        >>> schoenberg26 = serial.pcToToneRow(serial.getHistoricalRowByName(
        ...                                        'SchoenbergOp26').row)
        >>> schoenberg25.findZeroCenteredTransformations(schoenberg26)
        []
        >>> schoenberg26.findZeroCenteredTransformations(
        ...     schoenberg26.zeroCenteredTransformation('RI', 8))
        [('RI', 8)]
        '''
        if len(self) != len(otherRow):
            return False

        otherRowPitches = otherRow.pitchClasses()
        transformationList = []
        firstPitch = otherRowPitches[0]
        lastPitch = otherRowPitches[-1]

        if otherRowPitches == self.zeroCenteredTransformation('P', firstPitch).pitchClasses():
            transformation = 'P', firstPitch
            transformationList.append(transformation)
        if otherRowPitches == self.zeroCenteredTransformation('I', firstPitch).pitchClasses():
            transformation = 'I', firstPitch
            transformationList.append(transformation)
        if otherRowPitches == self.zeroCenteredTransformation('R', lastPitch).pitchClasses():
            transformation = 'R', lastPitch
            transformationList.append(transformation)
        if otherRowPitches == self.zeroCenteredTransformation('RI', lastPitch).pitchClasses():
            transformation = 'RI', lastPitch
            transformationList.append(transformation)

        return transformationList

    def findOriginalCenteredTransformations(self, otherRow):
        '''
        Gives the list of original-centered serial transformations taking one
        :class:`~music21.serial.ToneRow`
        to another, the second specified in the argument. Each transformation is given as a tuple
        of the transformation type and index.

        See :meth:`~music21.serial.originalCenteredTransformation` for an
        explanation of this convention.

        >>> chromatic = serial.pcToToneRow(       [2, 3, 4, 5, 6, 7, 8, 9, 'A', 'B',   0, 1])
        >>> reverseChromatic = serial.pcToToneRow([8, 7, 6, 5, 4, 3, 2, 1, 0,   'B', 'A', 9])
        >>> chromatic.findOriginalCenteredTransformations(reverseChromatic)
        [('I', 6), ('R', 7)]
        >>> schoenberg25 = serial.getHistoricalRowByName('SchoenbergOp25')
        >>> schoenberg26 = serial.getHistoricalRowByName('SchoenbergOp26')
        >>> schoenberg25.findOriginalCenteredTransformations(schoenberg26)
        []
        >>> schoenberg26.findOriginalCenteredTransformations(
        ...     schoenberg26.originalCenteredTransformation('RI',8))
        [('RI', 8)]
        '''
        # This is rather confused in execution.
        originalRowPitches = self.pitchClasses()
        otherRowPitches = otherRow.pitchClasses()
        transformationList = []
        oldFirstPitch = originalRowPitches[0]
        oldLastPitch = originalRowPitches[-1]
        newFirstPitch = otherRowPitches[0]

        # for T, I:
        tiPitch = (newFirstPitch - oldFirstPitch) % 12

        # for R
        rPitch = (newFirstPitch - oldLastPitch) % 12

        # for RI
        riPitch = (newFirstPitch - (2 * oldFirstPitch) + oldLastPitch) % 12

        # bound method
        ocTrans = self.originalCenteredTransformation

        if otherRowPitches == ocTrans('T', tiPitch).pitchClasses():
            transformation = ('T', tiPitch)
            transformationList.append(transformation)
        if otherRowPitches == ocTrans('I', tiPitch).pitchClasses():
            transformation = ('I', tiPitch)
            transformationList.append(transformation)
        if otherRowPitches == ocTrans('R', rPitch).pitchClasses():
            transformation = ('R', rPitch)
            transformationList.append(transformation)
        if otherRowPitches == ocTrans('RI', riPitch).pitchClasses():
            transformation = ('RI', riPitch)
            transformationList.append(transformation)

        return transformationList


# ----------------------------------------------------------------------------------------

class TwelveToneRow(ToneRow):
    '''
    A Stream representation of a twelve-tone row, capable of producing a 12-tone matrix.
    '''
    # row = None

    # _DOC_ATTR = {
    # 'row': 'A list representing the pitch class values of the row.',
    # }

    _DOC_ORDER = ['matrix', 'isAllInterval',
                  'getLinkClassification', 'isLinkChord', 'areCombinatorial']

#     def __init__(self, *arguments, **keywords):
#         super().__init__(*arguments, **keywords)
#         # environLocal.printDebug(['TwelveToneRow.__init__: length of elements', len(self)])
#
#         # if self.row != None:
#         #    for pc in self.row:
#         #        self.append(pitch.Pitch(pc))

    def matrix(self):
        '''
        Returns a :class:`~music21.serial.TwelveToneMatrix` object for the row.
        That object can just be printed (or displayed via .show())

        >>> src = serial.getHistoricalRowByName('SchoenbergOp37')
        >>> [p.name for p in src]
        ['D', 'C#', 'A', 'B-', 'F', 'E-', 'E', 'C', 'G#', 'G', 'F#', 'B']
        >>> len(src)
        12
        >>> s37 = serial.getHistoricalRowByName('SchoenbergOp37').matrix()
        >>> print(s37)
          0  B  7  8  3  1  2  A  6  5  4  9
          1  0  8  9  4  2  3  B  7  6  5  A
          5  4  0  1  8  6  7  3  B  A  9  2
          4  3  B  0  7  5  6  2  A  9  8  1
        ...
        >>> [str(e.pitch) for e in s37[0]]
        ['C', 'B', 'G', 'G#', 'E-', 'C#', 'D', 'B-', 'F#', 'F', 'E', 'A']


        '''
        # note: do not want to return a TwelveToneRow() type, as this will
        # add again the same pitches to the elements list twice.
        noteList = self.getElementsByClass('Note')

        i = [(12 - x.pitch.pitchClass) % 12 for x in noteList]
        matrix = [[(x.pitch.pitchClass + t) % 12 for x in noteList] for t in i]

        matrixObj = TwelveToneMatrix()
        i = 0
        for row in matrix:
            i += 1
            rowObject = copy.copy(self)
            rowObject.elements = []
            rowObject.id = 'row-' + str(i)
            for p in row:  # iterate over pitch class values
                n = note.Note()
                n.duration.quarterLength = 0.0
                n.pitch.pitchClass = p
                n.pitch.octave = None
                rowObject.append(n)
            matrixObj.insert(0, rowObject)

        # environLocal.printDebug([
        #  'calling matrix start: len row:', self.row, 'len self', len(self)])

        return matrixObj

    def findHistorical(self):
        '''
        Checks if a given :class:`music21.serial.TwelveToneRow` is the same as
        any of the historical
        twelve-tone rows stored by music21: see :func:`music21.serial.getHistoricalRowByName`.
        Returns a list of names of historical rows to which the input row is identical.

        >>> row = serial.pcToToneRow([2, 3, 9, 1, 11, 5, 8, 7, 4, 0, 10, 6])
        >>> row.findHistorical()
        ['SchoenbergOp32']
        >>> chromatic = serial.pcToToneRow(range(12))
        >>> chromatic.findHistorical()
        []
        '''
        sameRows = []
        for historicalRow in historicalDict:
            if self.isSameRow(getHistoricalRowByName(historicalRow)):
                sameRows.append(historicalRow)
        return sameRows

    def findTransformedHistorical(self, convention):
        '''
        Checks if a given :class:`music21.serial.TwelveToneRow` is a transformation of
        any of the historical
        twelve-tone rows stored by music21: see :func:`music21.serial.getHistoricalRowByName`.
        Returns a list
        of tuples, the tuple consisting of the name of a historical row, and a
        list of transformations relating
        the input row to the historical row.

        The convention for serial transformations must also be specified as 'zero' or
        'original', as explained
        in :meth:`~music21.serial.findZeroCenteredTransformations` and
        :meth:`~music21.serial.findOriginalCenteredTransformations`.

        >>> row = serial.pcToToneRow([5, 9, 11, 3, 6, 7, 4, 10, 0, 8, 2, 1])
        >>> row.findTransformedHistorical('original')
        [('SchoenbergOp32', [('R', 11)])]
        '''
        sameRows = []
        if convention == 'zero':
            for historicalRow in historicalDict:
                trans = getHistoricalRowByName(historicalRow).findZeroCenteredTransformations(self)
                if trans:
                    sameRows.append((historicalRow, trans))
            return sameRows
        if convention == 'original':
            for historicalRow in historicalDict:
                historicalRowObject = getHistoricalRowByName(historicalRow)
                trans = historicalRowObject.findOriginalCenteredTransformations(self)
                if trans:
                    sameRows.append((historicalRow, trans))
            return sameRows
        else:
            raise SerialException("Invalid convention - choose 'zero' or 'original'.")

    def isAllInterval(self):
        '''
        Describes whether or not a :class:`~music21.serial.TwelveToneRow` is an all-interval row.

        >>> chromatic = serial.pcToToneRow(range(12))
        >>> chromatic.pitchClasses()
        [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
        >>> chromatic.isAllInterval()
        False
        >>> bergLyric = serial.getHistoricalRowByName('BergLyricSuite')
        >>> bergLyric.pitchClasses()
        [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11]
        >>> bergLyric.isAllInterval()
        True
        '''

        if self.isTwelveToneRow() is False:
            raise SerialException('An all-interval row must be a twelve-tone row.')

        tempAllInterval = True
        intervalString = self.getIntervalsAsString()
        for i in range(1, 10):
            if str(i) not in intervalString:
                tempAllInterval = False
        if 'T' not in intervalString:
            tempAllInterval = False
        if 'E' not in intervalString:
            tempAllInterval = False
        return tempAllInterval

    def getLinkClassification(self):
        '''
        Gives the classification number of a Link Chord
        (as given in http://www.johnlinkmusic.com/LinkChords.pdf),
        that is, is an all-interval twelve-tone row containing a voicing of the
        all-trichord hexachord: [0, 1, 2, 4, 7, 8].
        In addition, gives a list of sets of five contiguous intervals
        within the row representing a voicing
        of the all-trichord hexachord. Note that the interval sets may be transformed.

        Named for John Link who discovered them.


        >>> bergLyric = serial.getHistoricalRowByName('BergLyricSuite')
        >>> bergLyric.pitchClasses()
        [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11]
        >>> bergLyric.isAllInterval()
        True
        >>> bergLyric.getLinkClassification()
        (None, [])
        >>> link = serial.pcToToneRow([0, 3, 8, 2, 10, 11, 9, 4, 1, 5, 7, 6])
        >>> link.getLinkClassification()
        (62, ['8352E'])
        >>> doubleLink = serial.pcToToneRow([0, 1, 8, 5, 7, 10, 4, 3, 11, 9, 2, 6])
        >>> doubleLink.getLinkClassification()
        (33, ['236E8', '36E8T'])
        '''
        # the link interval strings given below are untransformed: by inversion around 0,
        # original-centered retrograde, and
        # retrograde inversion around zero, we get three more link interval strings for
        # each one in fullLinkIntervals.
        # in the original rows, this corresponds simply to checking the interval string of any
        # inversion, retrograde inversion, and retrograde, respectively.

        fullLinkIntervals = ['125634T97E8', '134E78526T9', '134E79T6258', '134E79T6258',
                             '1367T89E254', '137E542896T', '137E982456T', '142965837ET',
                             '142973856ET', '1429738E65T', '14297TE6853', '145638E729T',
                             '1456T729E83', '1456T982E73', '145927E836T', '14598E63T72',
                             '14689T7E253', '1469E27T853', '149278356ET', '1492783E65T',
                             '1496258T73E', '1496E358T72', '14972836E5T', '14972E6385T',
                             '1497T853E62', '14E379T6528', '14E6T783529', '172E6853T94',
                             '17356ET8294', '1738T542E69', '173E65T8294', '1763T4952E8',
                             '176852E34T9', '179236E8T54', '179236E8T54', '17923E685T4',
                             '179245T8E63', '17924T586E3', '179T65234E8', '179T8E63254',
                             '179T8E63254', '1825E43796T', '1825E43796T', '1825E79T364',
                             '1825E79T364', '1852E43769T', '1852E79463T', '185629TE743',
                             '18563479TE2', '18563E7T492', '18734E5296T', '18734E5296T',
                             '187E259436T', '187E259436T', '18T352E7964', '18T497E3562',
                             '18T97E52364', '18T97E52364', '18E63T79452', '18E63T79452',
                             '19476538TE2', '1947T8536E2', '1954763T8E2', '19742538E6T',
                             '197425T6E83', '1974T8E6352', '197T8532E64', '1T5E7928364',
                             '1T63E874259', '1T6E3852479', '1T8352E4679', '1T974253E68',
                             '214367TE985', '214376598ET', '214376598ET', '2143E86597T',
                             '2149586E37T', '214976538ET', '214976538ET', '216734ET985',
                             '216743E9T85', '217634TE985', '21T8E956347', '21T96583E47',
                             '234T1596E87', '235189E647T', '235189E647T', '23689E7T145',
                             '236E981547T', '236E981547T', '23T514697E8', '2513647ET98',
                             '25189TE7463', '25189TE7463', '2546E981T73', '25691T8E473',
                             '2569E8T1437', '258T73E6149', '258T9614E37', '25T31496E87',
                             '25T89E61437', '2618T497E35', '26347ET9185', '263891T7E45',
                             '263891T7E45', '2653E718T49', '2654T1783E9', '2654T1783E9',
                             '2654E3871T9', '2654E3871T9', '2654E7T1983', '2654E7T1983',
                             '265819TE743', '2659E8T1347', '267431T8E95', '2694T817E35',
                             '269T1783E45', '269T1783E45', '269E3871T45', '269E3871T45',
                             '26E451T7389', '26E451T7389', '26E459817T3', '26E459817T3',
                             '26E4T718953', '26E4T718953', '26E873T5149', '26E95134T87',
                             '26E95178T43', '274316E985T', '274316E985T', '2743E86591T',
                             '274916E385T', '274916E385T', '2749586E31T', '276134ET985',
                             '276143E9T85', '27E34169T85', '2965387E41T', '2965387E41T',
                             '296E387T145', '29TE7436185', '29TE7463158', '29E7835641T',
                             '29E7835641T', '2E431T96587', '2E431T96587', '2E465387T19',
                             '2E637T85419', '2E783T51469', '2E783T51469', '2E796415T38',
                             '2E8T1956743', '2E9658T4137', '3142E8956T7', '3142ET79685',
                             '31456T972E8', '314672E9T85', '3152689TE74', '3152689TE74',
                             '3152E9T8764', '3158629TE74', '3158629TE74', '316452E98T7',
                             '317ET562894', '317ET926854', '317ET986254', '319765T42E8',
                             '3198265TE74', '31T524796E8', '31T567942E8', '31T7E294685',
                             '325E79T8164', '325E79T8164', '3265981TE74', '329E71T4568',
                             '329E71T4568', '32E981T6547', '347621T8E95', '3479TE26185',
                             '34T9E712568', '35146T927E8', '35146T927E8', '351T64927E8',
                             '351T64927E8', '351T7924E68', '35216E98T74', '3521T8E9674',
                             '3581629ET74', '3594T6127E8', '359E6128T74', '35E7216T498',
                             '35E72946T18', '35E729T6418', '3625189TE74', '3625189TE74',
                             '36524ET8917', '3674218T9E5', '36T154927E8', '36T154927E8',
                             '3764128T9E5', '38297E5T164', '38E729T6145', '3T17E924568',
                             '3T17E924568', '3T4952E8617', '3T6194527E8', '3T62E815497',
                             '3T97E528164', '3T97E528164', '3E2418596T7', '3E7T4926185',
                             '416352E7T98', '41T629E7835', '41T629E7835', '4328T56E917',
                             '4328TE65917', '43T9E865217', '463152E9T87', '46529E8T137',
                             '46731T8E925', '4692E513T87', '4692E513T87', '46982315ET7',
                             '469T315E287', '469T315E287', '4769E251T38', '4783T1629E5',
                             '47T198236E5', '47E928361T5', '4T1629E3785', '4TE86592317',
                             '4E2538T1697', '4E29658T317', '4E29658T317', '4ET85692317',
                             '4ET85692317', '5896T142E37']
        specialLinkIntervals = [
            '25634', '134E7', '134E7', 'E79T6', '89E25', '7E542', '7E982',
            '29658', '856ET', '8E65T', 'E6853', '8E729', '729E8', '982E7',
            '927E8', '8E63T', '7E253', '7T853', '78356', '783E6', '58T73',
            '358T7', '2836E', '2E638', '7T853', '79T65', '78352', 'E6853',
            '56ET8', '42E69', 'E65T8', '4952E', '52E34', '236E8', '36E8T',
            '3E685', 'T8E63', '586E3', '79T65', 'T8E63', '8E632', '25E43',
            '5E437', '25E79', '5E79T', 'E4376', 'E7946', '9TE74', '479TE',
            'E7T49', '734E5', '34E52', '87E25', 'E2594', '352E7', 'T497E',
            'T97E5', '97E52', '8E63T', 'T7945', '76538', '7T853', '4763T',
            '97425', '97425', 'T8E63', '7T853', '5E792', '74259', '52479',
            '8352E', '97425', '4367T', '43765', '76598', 'E8659', '586E3',
            '49765', '76538', '6734E', '21674', '7634T', '1T8E9', 'T9658',
            '34T15', '5189E', '189E6', '689E7', '6E981', 'E9815', '3T514',
            '47ET9', '25189', '9TE74', '6E981', '91T8E', '9E8T1', '58T73',
            'T9614', '5T314', '89E61', 'T497E', '47ET9', '891T7', '1T7E4',
            'E718T', 'T1783', '1783E', 'E3871', '3871T', '4E7T1', '7T198',
            '9TE74', '9E8T1', '1T8E9', 'T817E', 'T1783', '1783E', 'E3871',
            '3871T', '451T7', '1T738', '59817', '9817T', 'T7189', '71895',
            '3T514', '5134T', '5178T', '4316E', '16E98', 'E8659', '4916E',
            '16E38', '586E3', '6134E', '27614', '4169T', '65387', '5387E',
            '6E387', '9TE74', '9TE74', 'E7835', '78356', 'E431T', 'T9658',
            '65387', '37T85', '2E783', '3T514', '415T3', 'E8T19', '9658T',
            '3142E', '3142E', '56T97', '31467', '52689', '9TE74', '152E9',
            '58629', '9TE74', '52E98', '56289', '92685', '98625', '765T4',
            '98265', '52479', '56794', '31T7E', '25E79', '5E79T', '65981',
            '29E71', '9E71T', '2E981', '1T8E9', '479TE', 'T9E71', '146T9',
            '927E8', '1T649', '927E8', '51T79', '16E98', '1T8E9', '1629E',
            '94T61', 'E6128', '16T49', '946T1', '9T641', '25189', '9TE74',
            '36524', '36742', 'T1549', '927E8', '37641', '297E5', '8E729',
            'T17E9', '17E92', '4952E', '61945', '15497', 'T97E5', '97E52',
            '3E241', 'E7T49', '352E7', '629E7', 'E7835', '8T56E', '8TE65',
            '9E865', '152E9', '9E8T1', '1T8E9', '2E513', 'E513T', '2315E',
            'T315E', '315E2', '9E251', '1629E', '7T198', '8361T', '1629E',
            'E8659', 'E2538', '29658', '9658T', 'T8569', '85692', '142E3']
        linkClassification = [  # line breaks emphasize repetitions
            1, 2, 3, 3,
            4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
            18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
            30, 31, 32, 33, 33,
            34, 35, 36, 37, 38, 38,
            39, 39,
            40, 40, 41, 42, 43, 44, 45, 46, 46, 47, 47, 48, 49,
            50, 50,
            51, 51,
            52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
            64, 65, 65, 66, 67, 68, 68, 69, 70, 71, 72, 73, 74, 75, 75,
            76, 77, 77,
            78, 79, 80, 80,
            81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 90,
            91, 92, 92,
            93, 93,
            94, 94,
            95, 96, 97, 98, 99, 99,
            100, 100,
            101, 101,
            102, 102,
            103, 103,
            104, 105, 106, 107, 107, 108, 109, 109,
            110, 111, 112, 113, 114, 114,
            115, 116, 117, 118, 118,
            119, 119,
            120, 121, 122, 122,
            123, 124, 125, 126, 127, 128, 129, 130, 130,
            131, 132, 132,
            133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 142,
            143, 144, 144,
            145, 146, 147, 148, 149, 149,
            150, 150,
            151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 160,
            161, 162, 163, 163,
            164, 165, 166, 167, 167, 168, 169, 170, 171, 171,
            172, 173, 174, 175, 175,
            176, 177, 178, 179, 180, 181, 182, 182,
            183, 184, 184,
            185, 186, 187, 188, 189, 190, 191, 192, 192,
            193, 193,
            194]
        numChords = len(fullLinkIntervals)

        if self.isTwelveToneRow() is False:
            raise SerialException('A Link Chord must be a twelve-tone row.')

        rowChecklist = [self,
                        self.zeroCenteredTransformation('I', 0),
                        self.zeroCenteredTransformation('R', 0),
                        self.zeroCenteredTransformation('RI', 0)]
        specialIntervals = []
        classification = None
        for row in rowChecklist:
            intervals = row.getIntervalsAsString()
            for i in range(numChords):
                if fullLinkIntervals[i] == intervals:
                    classification = linkClassification[i]
                    specialIntervals.append(specialLinkIntervals[i])
        if not specialIntervals:
            return None, []
        else:
            return classification, specialIntervals

    def isLinkChord(self):
        '''
        Describes whether or not a :class:`~music21.serial.TwelveToneRow` is a Link Chord.

        >>> bergLyric = serial.getHistoricalRowByName('BergLyricSuite')
        >>> bergLyric.pitchClasses()
        [5, 4, 0, 9, 7, 2, 8, 1, 3, 6, 10, 11]
        >>> bergLyric.isAllInterval()
        True
        >>> bergLyric.isLinkChord()
        False
        >>> link = serial.pcToToneRow([0, 3, 8, 2, 10, 11, 9, 4, 1, 5, 7, 6])
        >>> link.isLinkChord()
        True
        >>> doubleLink = serial.pcToToneRow([0, 1, 8, 5, 7, 10, 4, 3, 11, 9, 2, 6])
        >>> doubleLink.isLinkChord()
        True
        '''
        linkTuple = self.getLinkClassification()
        if linkTuple[0] is None:
            return False
        else:
            return True

    def areCombinatorial(self, transType1, index1, transType2, index2, convention):
        '''
        Describes whether or not two transformations of a twelve-tone row are combinatorial.

        The first and second arguments describe one transformation, while the third and fourth
        describe another. One of the zero-centered or original-centered conventions for tone row
        transformations must be specified in the last argument; see
        :meth:`~music21.serial.zeroCenteredTransformation` and
        :meth:`~music21.serial.originalCenteredTransformation` explanations of these conventions.

        >>> moses = serial.getHistoricalRowByName('SchoenbergMosesAron')
        >>> moses.pitchClasses()
        [9, 10, 4, 2, 3, 1, 7, 5, 6, 8, 11, 0]
        >>> moses.areCombinatorial('P', 1, 'I', 4, 'zero')
        True
        >>> moses.areCombinatorial('R', 5, 'RI', 6, 'original')
        False
        '''
        if self.isTwelveToneRow() is False:
            raise SerialException('Combinatoriality applies only to twelve-tone rows.')

        if convention == 'zero':
            testRow = []
            trans1 = self.zeroCenteredTransformation(transType1, index1)
            pitches1 = trans1.pitchClasses()
            trans2 = self.zeroCenteredTransformation(transType2, index2)
            pitches2 = trans2.pitchClasses()
            for i in range(6):
                testRow.append(pitches1[i])
            for i in range(6):
                testRow.append(pitches2[i])
            return pcToToneRow(testRow).isTwelveToneRow()
        elif convention == 'original':
            testRow = []
            trans1 = self.originalCenteredTransformation(transType1, index1)
            pitches1 = trans1.pitchClasses()
            trans2 = self.originalCenteredTransformation(transType2, index2)
            pitches2 = trans2.pitchClasses()
            for i in range(6):
                testRow.append(pitches1[i])
            for i in range(6):
                testRow.append(pitches2[6 + i])
            return pcToToneRow(testRow).isTwelveToneRow()
        else:
            raise SerialException("Invalid convention - choose 'zero' or 'original'.")


class HistoricalTwelveToneRow(TwelveToneRow):
    '''
    Subclass of :class:`~music21.serial.TwelveToneRow` storing additional attributes of a
    twelve-tone row used in the historical literature.
    '''
    _DOC_ATTR = {
        'composer': 'The name of the composer.',
        'opus': 'The opus of the work, or None.',
        'title': 'The title of the work.',
    }

    composer = None
    opus = None
    title = None

    def __init__(self, composer=None, opus=None, title=None, row=None):
        super().__init__(row)
        self.composer = composer
        self.opus = opus
        self.title = title

    def _reprInternal(self):
        return '{} {} {}'.format(self.composer,
                                 self.opus,
                                 self.title)


def getHistoricalRowByName(rowName):
    '''
    Given the name referring to a twelve-tone row used in the historical literature,
    returns a :class:`~music21.serial.HistoricalTwelveToneRow` object with attributes
    describing the row.

    The names of the rows with stored attributes are below (each must be passed as a string,
    in single quotes).

    >>> for r in sorted(list(serial.historicalDict)):
    ...     print(r)
    BergChamberConcerto
    BergDerWein
    BergLulu
    BergLuluActIIScene1
    BergLuluActIScene20
    BergLyricSuite
    BergLyricSuitePerm
    BergViolinConcerto
    BergWozzeckPassacaglia
    SchoenbergFragOrganSonata
    SchoenbergFragPiano
    SchoenbergFragPianoPhantasia
    SchoenbergIsraelExists
    SchoenbergJakobsleiter
    SchoenbergMosesAron
    SchoenbergOp23No5
    SchoenbergOp24Mvmt4
    SchoenbergOp24Mvmt5
    SchoenbergOp25
    SchoenbergOp26
    SchoenbergOp27No1
    SchoenbergOp27No2
    SchoenbergOp27No3
    SchoenbergOp27No4
    SchoenbergOp28No1
    SchoenbergOp28No3
    SchoenbergOp29
    SchoenbergOp30
    SchoenbergOp31
    SchoenbergOp32
    SchoenbergOp33A
    SchoenbergOp33B
    SchoenbergOp34
    SchoenbergOp35No1
    SchoenbergOp35No2
    SchoenbergOp35No3
    SchoenbergOp35No5
    SchoenbergOp36
    SchoenbergOp37
    SchoenbergOp41
    SchoenbergOp42
    SchoenbergOp44
    SchoenbergOp45
    SchoenbergOp46
    SchoenbergOp47
    SchoenbergOp48No1
    SchoenbergOp48No2
    SchoenbergOp48No3
    SchoenbergOp50A
    SchoenbergOp50B
    SchoenbergOp50C
    WebernOp17No2
    WebernOp17No3
    WebernOp18No1
    WebernOp18No2
    WebernOp18No3
    WebernOp19No1
    WebernOp19No2
    WebernOp20
    WebernOp21
    WebernOp22
    WebernOp23
    WebernOp24
    WebernOp25
    WebernOp26
    WebernOp27
    WebernOp28
    WebernOp29
    WebernOp30
    WebernOp31
    WebernOpNo17No1

    >>> web = serial.getHistoricalRowByName('WebernOp29')
    >>> web.row
    [3, 11, 2, 1, 5, 4, 7, 6, 10, 9, 0, 8]
    >>> web.composer
    'Webern'
    >>> web.opus
    'Op. 29'
    >>> web.title
    'Cantata I'
    >>> web.isLinkChord()
    False

    NOTE: before v.6, these rows had 'Row' in front of them,
    like 'RowWebernOp29' instead of 'WebernOp29'.  They can still be accessed
    by the old name.

    >>> rowWeb = serial.getHistoricalRowByName('RowWebernOp29')
    >>> rowWeb.row == web.row
    True
    '''
    if rowName.startswith('Row'):
        rowName = rowName[3:]

    if rowName in historicalDict:
        attr = historicalDict[rowName]
        rowObj = HistoricalTwelveToneRow(attr[0], attr[1], attr[2], attr[3])
        return rowObj
    else:
        raise SerialException('No historical row with given name found')

# ------------------------------------------------------------------------------


def pcToToneRow(pcSet):
    '''
    A convenience function that, given a list of pitch classes represented as integers
    and turns it in to a :class:`~music21.serial.ToneRow` object.

    >>> chromaticRow = serial.pcToToneRow([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
    >>> chromaticRow.show('text')
    {0.0} <music21.note.Note C>
    {1.0} <music21.note.Note C#>
    {2.0} <music21.note.Note D>
    {3.0} <music21.note.Note E->
    {4.0} <music21.note.Note E>
    {5.0} <music21.note.Note F>
    {6.0} <music21.note.Note F#>
    {7.0} <music21.note.Note G>
    {8.0} <music21.note.Note G#>
    {9.0} <music21.note.Note A>
    {10.0} <music21.note.Note B->
    {11.0} <music21.note.Note B>
    >>> matrixObj = chromaticRow.matrix()
    >>> print(matrixObj)
      0  1  2  3  4  5  6  7  8  9  A  B
      B  0  1  2  3  4  5  6  7  8  9  A
    ...

    >>> fancyRow = serial.pcToToneRow([4, 5, 0, 6, 7, 2, 'a', 8, 9, 1, 'b', 3])
    >>> matrixObj = fancyRow.matrix()
    >>> print(matrixObj)
      0  1  8  2  3  A  6  4  5  9  7  B
      B  0  7  1  2  9  5  3  4  8  6  A
    ...

    Note that the Row does not have to be a valid row to exist:

    >>> multiSetRow = serial.pcToToneRow([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
    >>> multiSetRow.pitchClasses()
    [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

    Or even have 12 notes:

    >>> shortRow = serial.pcToToneRow([3, 4])
    >>> shortRow.pitchClasses()
    [3, 4]

    If the row does have twelve notes (whether unique or not) the object returned
    is a `TwelveToneRow`:

    >>> multiSetRow
    <music21.serial.TwelveToneRow 111111111111>

    Otherwise, it is simply a `ToneRow`:

    >>> shortRow
    <music21.serial.ToneRow 34>
    '''
    if len(pcSet) == 12:
        a = TwelveToneRow()
    else:
        a = ToneRow()

    for thisPc in pcSet:
        n = note.Note()
        n.pitch.pitchClass = thisPc
        n.pitch.octave = None
        a.append(n)
    return a


def rowToMatrix(p: List[int]) -> str:
    '''
    Takes a list of numbers of converts it to a string representation of a
    12-tone matrix.

    >>> aMatrix = serial.rowToMatrix([0, 2, 11, 7, 8, 3, 9, 1, 4, 10, 6, 5])
    >>> print(aMatrix)
      0  2 11  7  8  3  9  1  4 10  6  5
     10  0  9  5  6  1  7 11  2  8  4  3
      1  3  0  8  9  4 10  2  5 11  7  6
      5  7  4  0  1  8  2  6  9  3 11 10
      4  6  3 11  0  7  1  5  8  2 10  9
      9 11  8  4  5  0  6 10  1  7  3  2
      3  5  2 10 11  6  0  4  7  1  9  8
     11  1 10  6  7  2  8  0  3  9  5  4
      8 10  7  3  4 11  5  9  0  6  2  1
      2  4  1  9 10  5 11  3  6  0  8  7
      6  8  5  1  2  9  3  7 10  4  0 11
      7  9  6  2  3 10  4  8 11  5  1  0

    This function survives today (2020) because it's been
    an example function for `music21` since the very first demonstrations
    of predecessors from around 2000 onwards.  Nowadays, better to create
    a `TwelveToneRow()` object and then get a matrix from that:

    >>> ttr = serial.TwelveToneRow([0, 2, 11, 7, 8, 3, 9, 1, 4, 10, 6, 5])
    >>> matrix = ttr.matrix()
    >>> print(matrix)
      0  2  B  7  8  3  9  1  4  A  6  5
      A  0  9  5  6  1  7  B  2  8  4  3
      1  3  0  8  9  4  A  2  5  B  7  6
      5  7  4  0  1  8  2  6  9  3  B  A
      4  6  3  B  0  7  1  5  8  2  A  9
      9  B  8  4  5  0  6  A  1  7  3  2
      3  5  2  A  B  6  0  4  7  1  9  8
      B  1  A  6  7  2  8  0  3  9  5  4
      8  A  7  3  4  B  5  9  0  6  2  1
      2  4  1  9  A  5  B  3  6  0  8  7
      6  8  5  1  2  9  3  7  A  4  0  B
      7  9  6  2  3  A  4  8  B  5  1  0
    '''

    i = [(12 - x) % 12 for x in p]
    matrix = [[(x + t) % 12 for x in p] for t in i]

    ret = []
    for row in matrix:
        msg = []
        for thisPC in row:
            msg.append(str(thisPC).rjust(3))
        ret.append(''.join(msg))

    return '\n'.join(ret)


# ------------------------------------------------------------------------------
class Test(unittest.TestCase):

    def runTest(self):
        pass

#    def testRows(self):
#        from music21 import interval
#
#        self.assertEqual(len(vienneseRows), 71)
#
#        totalRows = 0
#        cRows = 0
#        for thisRow in vienneseRows:
#            thisRow = thisRow()
#            self.assertIsInstance(thisRow, TwelveToneRow)
#
#            if thisRow.composer == 'Berg':
#                continue
#            post = thisRow.title
#
#            totalRows += 1
#            if thisRow[0].pitchClass == 0:
#                cRows += 1

#             if interval.notesToInterval(thisRow[0],
#                                    thisRow[6]).intervalClass == 6:
#              # between element 1 and element 7 is there a TriTone?
#              rowsWithTTRelations += 1

    def testMatrix(self):
        src = getHistoricalRowByName('SchoenbergOp37')
        self.assertEqual([p.name for p in src],
                         ['D', 'C#', 'A', 'B-', 'F', 'E-', 'E', 'C', 'G#', 'G', 'F#', 'B'])
        s37 = getHistoricalRowByName('SchoenbergOp37').matrix()
        r0 = s37[0]
        # r0 is TOO an iterable
        # pylint: disable=not-an-iterable
        self.assertEqual([e.name for e in r0], ['C', 'B', 'G', 'G#', 'E-', 'C#', 'D', 'B-',
                                                    'F#', 'F', 'E', 'A'])

    def testLabelingA(self):
        from music21 import corpus
        series = {'a': 1, 'g-': 2, 'g': 3, 'a-': 4,
                  'f': 5, 'e-': 6, 'e': 7, 'd': 8,
                  'c': 9, 'c#': 10, 'b-': 11, 'b': 12}
        s = corpus.parse('bwv66.6')
        for n in s.flat.notes:
            for key in series:
                if n.pitch.pitchClass == pitch.Pitch(key).pitchClass:
                    n.addLyric(series[key])
        match = []
        for n in s.parts[0].flat.notes:
            match.append(n.lyric)
        self.assertEqual(match, ['10', '12', '1', '12', '10', '7', '10', '12', '1', '10', '1',
                                 '12', '4', '2', '1', '12', '12', '2', '7', '1', '12', '10',
                                 '10', '1', '12', '10', '1', '4', '2', '4', '2', '2', '2',
                                 '2', '2', '5', '2'])
        # s.show()

    def testHistorical(self):
        nonRows = []
        for historicalRow in historicalDict:
            if getHistoricalRowByName(historicalRow).isTwelveToneRow() is False:
                nonRows.append(historicalRow)
        self.assertEqual(nonRows, [])

    def testExtractRowParts(self):
        '''Was a problem in slices'''
        aRow = getHistoricalRowByName('BergViolinConcerto')
        unused_aRow2 = aRow[0:3]

    def testPostTonalDocs(self):
        aRow = getHistoricalRowByName('BergViolinConcerto')
        # aMatrix = aRow.matrix()
        bStream = stream.Stream()
        for i in range(0, 12, 3):
            aRow2 = aRow[i:i + 3]
            c = chord.Chord(aRow2)
            c.addLyric(c.primeFormString)
            c.addLyric(c.forteClass)
            bStream.append(c)

    def testCopyAndDeepcopy(self):
        '''
        Test copying all objects defined in this module
        '''
        import sys
        import types
        for part in sys.modules[self.__module__].__dict__:
            match = False
            for skip in ['_', '__', 'Test', 'Exception']:
                if part.startswith(skip) or part.endswith(skip):
                    match = True
            if match:
                continue
            obj = getattr(sys.modules[self.__module__], part)
            if callable(obj) and not isinstance(obj, types.FunctionType):
                i = copy.copy(obj)
                j = copy.deepcopy(obj)


# ------------------------------------------------------------------------------
# define presented order in documentation
_DOC_ORDER = ['ToneRow', 'TwelveToneRow', 'HistoricalTwelveToneRow', 'ContiguousSegmentOfNotes',
              'historicalDict',
              'pcToToneRow', 'TwelveToneMatrix', 'rowToMatrix', 'getHistoricalRowByName',
              ]

if __name__ == '__main__':
    import music21
    music21.mainTest(Test)

